It is possible to drag one skeleton into another: select the main parent bone that is not the root, and drag and drop it from one skeleton to another within the same project for this to happen. You'd need to recreate any constraints, and also reimport animations, but it's doable.
As Nate pointed out, it may make more sense to have separate skeletons. My approach would be to have 3 skeletons (or two if the bed base and pillow don't move):
One for the character, one for the bedsheets, and one for the base of the bed and pillow. You can have them within the same project, and if each has an animation that you call the same, you can easily animate them to be in sync within the Spine editor.
I hope this helps!
